[amp_mcq option1=”S1″ option2=”S2″ option3=”S3″ option4=”S4″ correct=”option1″]
Signal processing
12. The amplitude spectrum of a Gaussian pulse is
[amp_mcq option1=”Uniform” option2=”A sine function” option3=”Gaussian” option4=”An impulse function” correct=”option3″]
Detailed SolutionThe amplitude spectrum of a Gaussian pulse is
13. A discrete-time all-pass system has two of its poles at 0.25<0° and 2<30°. Which one of the following statements about the system is TRUE?
[amp_mcq option1=”It has two more poles at 0.5<30° and 4<0°” option2=”It is stable only when the impulse response is two-sided” option3=”It has constant phase response over all frequencies” option4=”It has constant phase response over the entire z-plane” correct=”option3″]
14. A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s – 6}}.$$ To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is
[amp_mcq option1=”s + 3″ option2=”s – 2″ option3=”s – 6″ option4=”s + 1″ correct=”option1″]
15. Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is \[\xrightarrow{{U\left( s \right)}}\boxed{\frac{1}{s}}\xrightarrow{{Y\left( s \right)}}\]
[amp_mcq option1=”u(t)” option2=”tu(t)” option3=”$$\frac{{{t^2}}}{2}u\left( t \right)$$” option4=”e-tu(t)” correct=”option3″]
16. The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,
[amp_mcq option1=”$$\frac{1}{2},\frac{1}{2}x\left( t \right)$$” option2=”$$ – \frac{1}{2},\frac{1}{2}x\left( t \right)$$” option3=”$$\frac{1}{2}, – \frac{1}{2}x\left( t \right)$$” option4=”$$ – \frac{1}{2}, – \frac{1}{2}x\left( t \right)$$” correct=”option1″]
17. Laplace transforms of the functions tu(t) and u(t)sin(t) are respectively
[amp_mcq option1=”$${1 \over {{s^2}}},{s \over {{s^2} + 1}}$$” option2=”$${1 \over s},{1 \over {{s^2} + 1}}$$” option3=”$${1 \over {{s^2}}},{1 \over {{s^2} + 1}}$$” option4=”$$s,{s \over {{s^2} + 1}}$$” correct=”option1″]
Detailed SolutionLaplace transforms of the functions tu(t) and u(t)sin(t) are respectively
18. It is desired to find three-tap causal filter which gives zero signal as an output to and input of the form \[x\left[ n \right] = {c_1}\exp \left( { – \frac{{j\pi n}}{2}} \right) + {c_2}\exp \left( {\frac{{j\pi n}}{2}} \right),\] Where c1 and c2 are arbitrary real numbers. The desired three-tap filter is given by h[0] = 1, h[1] = a, h[2] = b and h[n] = 0 for n < 0 or n > 2. What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above? \[\xrightarrow{{x\left[ n \right]}}\boxed{\begin{array}{*{20}{c}} {n = 0} \\ \downarrow \\ {h\left[ n \right] = \left\{ {1,a,b} \right\}} \end{array}}\xrightarrow{{y\left[ n \right] = 0}}\]
[amp_mcq option1=”a = -1, b = 1″ option2=”a = 0, b = 1″ option3=”a = 1, b = 1″ option4=”a = 0, b = -1″ correct=”option3″]
19. Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z).
[amp_mcq option1=”0.5 – j0.25″ option2=”$${1 \over {\left( {0.5 + j0.25} \right)}}$$” option3=”$${1 \over {\left( {0.5 – j0.25} \right)}}$$” option4=”2 + j4″ correct=”option1″]
20. The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ {1,} & {{\rm{if}}\,a \le t \le b} \cr 0 & {{\rm{otherwise}}} \cr } } \right.$$ is
[amp_mcq option1=”$${{a – b} \over s}$$” option2=”$${{{e^z}\left( {a – b} \right)} \over s}$$” option3=”$${{{e^{ – as}} – {e^{ – bs}}} \over s}$$” option4=”$${{{e^{ – \left( {a – b} \right)}}} \over s}$$” correct=”option4″]